Linear social interactions models where agents’ payoffs depend on the average action of the observed peers have opened new areas of research in economics ranging from education to industrial organization. In this paper, we propose a novel interpretation of the Nash equilibrium based on a Markov process that evolves according to the neighboring relations in a social network. By means of this interpretation, we give a new pairwise connectivity measure and a overall centrality measure which disentangles the effects of network’s topology and agents’ heterogeneity that were missing in the dominant centrality measure used in this literature (Bonacich centrality). Also, this Markov approach allows to decompose equilibrium action into a structural effect given by the Markov process’ stationary probability distribution common to all agents and an agent specific effect related to her location in the network. Finally, we show that this approach can be used in non-linear models, with examples in education and macroeconomics.